Method and system for controlling rate of change of ratio in a continuously variable transmission

ABSTRACT

Systems and methods for efficiently and effectively controlling the rate of change of ratio, not simply the ratio, in a CVT. By controlling the rate of change of ratio, the acceleration or deceleration of a vehicle can be controlled in an efficient manner. Furthermore, the rate of change of ratio can be controlled by controlling the clamping pressure of the pulleys and/or differential pressure between the pulleys with minimal slip by using a servo control mechanism adapted for control by a system controller based on equilibrium mapping and other control parameters.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/830,290 filed on Jul. 30, 2007, now U.S. Pat. No. 7,713,166,incorporated herein by reference in its entirety, which is acontinuation of U.S. patent application Ser. No. 10/804,814 filed onMar. 19, 2004, now U.S. Pat. No. 7,261,672 issued on Aug. 28, 2007,incorporated herein by reference in its entirety, which claims priorityfrom U.S. provisional patent application Ser. No. 60/456,226 filed onMar. 19, 2003, incorporated herein by reference in its entirety, andfrom U.S. provisional patent application Ser. No. 60/457,453 filed onMar. 24, 2003, incorporated herein by reference in its entirety.

This application is also related to PCT International Publication NumberWO/2004/083870, published on Sep. 30, 2006, incorporated herein byreference in its entirety.

This application is also related to U.S. Patent Application PublicationNo. US 2004/0254047 A1 published on Dec. 16, 2004, incorporated hereinby reference in its entirety.

This application is also related to U.S. Patent Application PublicationNo. US 2008/0032858 A1 published on Feb. 7, 2008, incorporated herein byreference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC

Not Applicable

COPYRIGHT PROTECTION

A portion of the material in this patent document is subject tocopyright protection under the copyright laws of the United States andof other countries. The owner of the copyright rights has no objectionto the facsimile reproduction by anyone of the patent document or thepatent disclosure, as it appears in the United States Patent andTrademark Office publicly available file or records, but otherwisereserves all copyright rights whatsoever. The copyright owner does nothereby waive any of its rights to have this patent document maintainedin secrecy, including without limitation its rights pursuant to 37C.F.R. §1.14.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention pertains generally to controlling the operation of acontinuously variable transmission, and more particularly to a methodand system for controlling, for example, the clamping and differentialpressures in a continuously variable transmission to achieve a desiredrate of change of ratio.

2. Description of Related Art

This application incorporates by reference U.S. Pat. Nos. 6,116,363,6,054,844, 5,842,534, PCT International Publication No. WO 00/25417, PCTInternational Publication No. WO 02/058209 A1, and PCT InternationalPublication No. WO 00/12918, each of which is related to thisapplication.

The concept of an engine and a “continuously variable transmission” is avery old concept invented in the 1900's, but the theoretical efficiencyof the engine, performance and drivability could never be obtainedautomatically. This can be seen with reference to the conventionalpowertrain and transmission shown in FIG. 1 where an internal combustionengine 10 has an output shaft 12 that drives a decoupling/startingclutch or torque converter 14, which is in turn coupled to the inputshaft 16 of a continuously variable transmission (CVT) or automatictransmission (AT) 18, which in turn has an -output driving a drive shaftor differential 20 coupled to a final drive wheel 22 (e.g., axle andtire). The deficiencies of such a configuration are caused by thedynamic equation representing the engine/CVT system:

${\alpha_{DS} = \frac{{{- \overset{\circ}{R}}I_{E}S_{E}} + {T_{E}R} - T_{loss} - T_{RL}}{I_{DS} + {R^{2}I_{E}}}},{\overset{\circ}{R} = \frac{\mathbb{d}R}{\mathbb{d}t}}$where α_(DS)=acceleration of the vehicle reflected to the drive shaft,

${R = \frac{S_{E}}{S_{DS}}},$I_(E)=engine inertia, I_(DS)=vehicle inertia at the driveshaft,S_(E)=engine speed, S_(DS)=drive shaft speed, T_(E)=engine torque,T_(loss) torque losses, and T_(RL)=road load torque at the driveshaft.Because the first term—

I_(E)S_(E) and the second term T_(E)R generally oppose each other, theacceleration of the car and the torque and speed of the engine aredifficult to control simultaneously. As a result, the best efficiencyand minimum emissions for a gasoline or diesel engine cannot be realizedwithout a sacrifice in performance. This can be seen with furtherreference to FIG. 2 and FIG. 3 which show operating characteristics ofthe engine as a function of engine speed and torque, where WOT=wide openthrottle and denotes the maximum torque line, IOL=ideal torque/speedoperating line and denotes where the best efficiency and/or leastemissions (minimum brake specific fuel consumption or BSFC) occurs, andPOL=practical operating line due to engine/transmission characteristics.Note in FIG. 3 that point A is less efficient than point B but must beused to provide proper vehicle behavior (transient performance).

As discussed in PCT International Publication No. WO 00/25417, theforegoing deficiencies can be overcome, for example, by inserting anelectric motor or motor/generator, a battery, and associated controlsbetween the engine and the continuously variable or automatictransmission. More particularly, a motor/generator is controlled tocounteract the negative effect of the—

I_(E)S_(E) in the dynamic equation. The motor/generator can then be usedto allow the engine to operate at “wide open throttle” (WOT), or alongthe “Ideal Torque/Speed Operating Line” (IOL) for best efficiency andlowest emissions, or along any other predetermined operation line. Inthis way, the engine can be run continuously while energy flows into orout of the battery energy storage system connected to the electricmotor/generator. If the battery is large enough to drive the vehicle along distance, then the efficiency of energy into and out of the batteryis high since the battery internal resistance is low. The emissions ofthe gasoline or diesel engine can be controlled effectively because theengine is operated at high load consistently. This approach ensures thatthe gasoline or diesel engine is never operated at closed throttle athigh speeds or operated at low efficiency low load conditions. If thepower required is lower than the minimum power of the engine on the IOL,the engine is automatically decoupled and stopped (or idled if desired),and the vehicle is operated as an electric vehicle.

More particularly, FIG. 4 shows an electric motor 24 coupled to theinput shaft 16 of the continuously variable transmission 18 so that itinjects power in parallel with the drive train between engine 10 andcontinuously variable transmission 18. Electric motor 24 is powered by abattery 26, which would typically comprise a bank of batteries,ultra-capacitors or the like, such as those used in electric vehicles.Operation of electric motor 24 is controlled by a motor controller 28,which is a conventional electronic armature controller or the like,which is in turn controlled by a microprocessor or other computer-basedprogrammable system controller 30.

System controller 30 processes a plurality of control and feedbacksignals. As shown, the primary input control signals are from thevehicle accelerator pedal 32 and brake pedal 34. Based on these signals,system controller 30 sends a throttle control signal 36 to engine 10 tocontrol the engine torque T_(E), an engine engagement on/off signal 38to clutch 14, a torque control signal 42 to motor controller 28 tocontrol motor torque T_(M), and a rate of change of speed ratio controlsignal 44 to control the rate of change

 of the speed ratio R of continuously variable transmission 18, where

${R = \frac{S_{E}}{S_{DS}}},$S_(E)=engine speed and S_(DS)=driveshaft speed. It should be noted thatS _(DS) =S _(CAR) ×Cwhere S_(CAR) is the speed of the vehicle and C is a constant dependenton the gear ratio of the final drive and tire radius for the vehicle. Atthe same time, system controller 30 senses engine speed S_(E) via speedsignals 40, the ratio R via signals 46, and vehicle speed S_(CAR) viasignals 48. Note that the system controller 30 may send an “on/off”signal to engine 10, but a separate starter motor is not needed;electric motor 24 can be used start engine 10 because it is coupled toengine output shaft 12 through clutch 14. The engine 10 may be turned“off” or idled when clutch 14 is opened.

Referring to FIG. 5, it will also be appreciated that the foregoingtechniques can be extended to a series hybrid vehicle configuration asshown in which a generator 50 is used to provide charging capability forbattery 26 as well as to provide a braking effect for engine 10 duringdeceleration. Operation of generator 50 is preferably controlled by agenerator controller 52, which is a conventional electronic armaturecontroller or the like. Generator controller 52 controls generatortorque, T_(G), in response to signals received from system controller 30through torque control line 54. Note that T_(G)=T_(E) in thisconfiguration. Note also the inclusion of an optional starter controlline 56 for starting and shutting down engine 10.

Note that operation of the engine in the above configuration isconsiderably different than in a series hybrid vehicle where the engineis always running at one speed. When the engine is operated at aconstant speed, the efficient power output only occurs at one level.Thus the batteries will have to absorb excess power or provideadditional power to drive the vehicle. This results in considerable deepbattery cycling and attendant inefficiencies. In the systems shown inFIG. 4 and FIG. 5, the engine is used more and the batteries are shallowcycled. Because the amount of power cycled by the batteries is greatlyreduced with the present invention, the range per battery charge isincreased. Battery life is increased as well.

Referring now to FIG. 4, FIG. 6, and FIG. 7 together, system controller30 implements the control and sensing functions of the system usingconventional hardware and/or software. In FIG. 6, A_(C)=acceleratorpedal position and represents power or torque commanded by the driver(P_(C) or +T_(C), respectively); B_(C)=brake pedal position representingnegative torque commanded by the driver (−T_(C)); T_(M)=electric motortorque; P_(EP)=the error or difference between the power commanded bythe driver and the power along the IOL for the power control mode(P_(C)−P_(IOL)); T_(EP)=the error or difference between the torquecommanded by the driver and the torque along the IOL for the torquecontrol mode

$\left( {T_{C} - \frac{P_{IOL}}{S_{E}}} \right);$P_(IOLE)=the power along the ideal operating line of the engine;P_(IOLM)=the power along the ideal operating line of the electric motor;IRL=the ideal regeneration line for braking; T_(EB)=the error ordifference between the braking commanded by the driver and the brakingalong the IRL for the braking control mode (B_(C)−T_(IRL)); T_(IRL)=thetorque along the ideal regeneration line for braking; K₁=a gainadjustment for desired response time and stability of the circuit, K₂=again adjustment set in response to S_(E)

 in order to achieve the desired response characteristics in FIG. 7,T=the time constant of the filter, S=the Laplace transform of variableP_(EP) or T_(E) which is easily programmed by those skilled in the art;R=the ratio between engine speed and driveshaft speed;

=the rate of change of ratio R; C=a conversion constant to convertvehicle speed to driveshaft speed; S_(E)=engine speed; S_(OS)=driveshaft speed; S_(CAR)=vehicle speed; and K_(B) is a gain value forscaling. When the accelerator pedal is depressed, switches SW1 and SW2go to the accelerator position. Switches SW3 and SW4 will be setaccording to whether the vehicle is in the electric or hybrid mode.Similarly, when the brake pedal is depressed, switches SW1 and SW2 go tothe brake position. Each of these switches generally may be softwareswitches in system controller 30. The IOL_(E) of the engine is obtainedby testing the engine to determine the best efficiency and emissions ateach speed. The IOL_(M) and IRL are obtained by testing the electricmotor/generator and battery system to obtain the most energy into thebattery at each speed. Note that the IOL_(M) is used when the vehicle isin the electric drive mode where the vehicle is operated, generally,below freeway speeds until the batteries are depleted to a predeterminedstate as, for example, described in U.S. Pat. No. 5,842,534.

There are also many possible control algorithms for hybrid electricvehicles. The control objective in the above example is to drive thevehicle using electric energy until the internal combustion engine isturned “on” and then to drive the vehicle with the internal combustionengine as much as possible, automatically supplementing the internalcombustion engine with electric energy when needed to maintain operationof the engine along the IOL. Significantly, energy may be put back intothe batteries temporarily when the engine power is reduced in order tokeep the engine on the IOL at all times in the hybrid mode. This kind ofoperation can significantly reduce emissions and increase engineefficiency.

In operation, system controller 30 senses the acceleration command A_(C)from the accelerator pedal and the switches SW1 and SW2 shown in FIG. 6go to the accelerator position. When power or a positive torque iscommanded by the driver (P_(C) or +T_(C)) in the electric vehicle modedetermined by SW3 and SW4 as the case may be depending upon whether ornot the system is operating in the power control region or the torquecontrol region shown in FIG. 7, the system is in an acceleration modeand the desired motor torque T_(M) is then determined at 114 accordingto

$T_{M} = {{\frac{P_{C}}{S_{E}} + {K_{2}S_{E}\overset{\circ}{R}\mspace{14mu}{or}\mspace{14mu} T_{M}}} = {T_{C} + {K_{2}S_{E}\overset{\circ}{R}}}}$If the vehicle is in the hybrid-mode, then T_(M) is determined at 126according to

$T_{M} = {{\frac{P_{C}}{S_{E}} - T_{{IOL}_{E}} + {K_{2}S_{E}\overset{\circ}{R}\mspace{14mu}{or}\mspace{14mu} T_{M}}} = {T_{C} - T_{{IOL}_{E}} + {K_{2}S_{E}\overset{\circ}{R}}}}$The motor torque signal determined above is sent to motor controller 28in FIG. 4 to vary the speed and power of engine 10 and to drive the car.The resultant change in electric motor torque in turn affects thevehicle dynamics at 102, which affect engine speed, vehicle speed andthe ratio R at CVT 18. Taking the speed of the vehicle S_(CAR) as wellas the ratio R at 102, in FIG. 6, engine speed S_(E) (which may also bethe same as the motor speed S_(M) where they are on a common shaft) canbe determined by applying a conversion constant C to the vehicle speedS_(CAR) at 104 to get the speed S_(DS) of driveshaft 20 of FIG. 4 (whichis the output of CVT 18) and then multiplying the driveshaft speedS_(DS) by the ratio R at 106 in FIG. 6 to give the engine speed S_(E).Now having engine speed S_(E), at 108, 116 and 128 look-up tablescontaining the IOL entries for the hybrid mode, braking mode and theelectric mode, respectively, are accessed to determine the ideal enginepower or torque output level for the given speed. Then, at 110 for thehybrid mode, 118 for the braking mode or 130 for the electric mode, theoutput of the corresponding look-up table is compared with either thepower P_(C) (if in power control mode) or positive torque+T_(C) (if intorque control mode) commanded by the driver with the accelerator pedalas sensed from accelerator pedal position A_(C) to determine a powererror P_(EP) or a torque error T_(EP). The corresponding error signal isthen used to affect the rate of change

 of the ratio R after filtering the signal at 112. CVT 18 of FIG. 4 thusresponds in accordance with the adjustment of the rate of change ofratio,

.

Note that an important aspect of the control system is the control ofthe rate of change of the ratio R; that is, the control of

. This is accomplished by filtering the error signal between thecommanded power PC or torque TC and the IOL power or torque. The signalfiltering, which is in the form of

$K_{1} \cdot \frac{1}{{TS} + 1}$is well known in the art of electrical engineering. It is understoodthat this filter is only representative of one form that may be placedat this point, and in practice the filter may include both linear andnon-linear elements. The purpose of the filter is to allow the designerto control the ratio rate,

. It is undesirable to change R quickly and, therefore, a filter isnecessary to provide the desired system response. The values of K₁ and Tare heuristically determined, as is the form of the filter (which isshown here as first order). Those skilled in the art will appreciatethat filters of many other representations will work and can be selecteddepending on the desired response.

During braking, torque is being commanded at the wheels rather thanengine power. Here, system controller 30 senses the braking commandB_(C) from the brake pedal. When the driver commands negative torque−T_(C), the system is in a deceleration (regeneration) mode and theswitches go to the brake position. Here, control of the CVT and electricmotor/generator reverses to produce a negative torque on the driveshaft,thus braking the vehicle. The operation of the braking circuit issimilar to that of the accelerator circuit except for the use of theideal regeneration line IRL, which reflects the highest efficiency for agiven power for regenerating energy into the batteries by the electricmotor/generator.

For purposes of braking, the desired motor torque T_(M) is determined at100 according to

$T_{M} = {\frac{T_{C}}{R} - {K_{2}S_{E}\overset{\circ}{R}}}$and the signal is sent to motor/generator controller 28 to vary thespeed and power of engine 10. The resultant change in electricmotor/generator and engine torque again affect the vehicle dynamics at102, to slow the car which affects motor and/or engine speed, vehicledeceleration and the ratio R at CVT 18. Here, however, engine speedS_(E) is used at 116 to access a look-up table containing entriesrepresenting the IRL, which is also an empirically determined table.Then, at 118, the output of the look-up table is compared with thenegative torque −T_(C) commanded by the driver with the brake pedal assensed from brake pedal position B_(C) to determine the braking torqueerror T_(EB). The braking torque error signal T_(EB) is then scaled by avalue of K_(B) through gain box 120 and used to affect the rate ofchange

 of the ratio R after filtering at 112. It should be appreciated thatthe filtering in the brake torque control can be different if desiredand that gain box 120 may contain additional filters.

As can be seen, therefore, FIG. 6 and FIG. 7 represent the controls forthe configuration shown in FIG. 4 and, in principle, the controls forthe configurations shown in FIG. 5 or other hybrid electric drivesystems.

Consider typical operation shown in FIG. 7 in conjunction with thecontrol diagram of FIG. 6. Assume that the vehicle is cruising at afixed speed when the engine is supplying all the power to drive thevehicle and the electric motor/generator is supplying no power. Considerpoint A in FIG. 7 in this condition of steady state operation whereP_(EP)=0 and P_(C)=P_(IOL) is reached with the accelerator pedalposition at A_(CA). If the driver suddenly depresses the pedal to asecond position, which will be designated as A_(CB), meaning the driverwants to increase power, the torque increases instantly to point B alongline L₁ with torque supplied by the electric motor and battery. This isso because P_(EP) is now greater than P_(IOL). Then T_(M) is computed inblock 114 if the vehicle is in the electric mode or block 126 if vehicleis in the hybrid mode. It will be appreciated that at this instant that

=0. Then P_(C)/S_(E) supplies all necessary torque in electric mode andP_(C)/S_(E)−T_(IOLE) or T_(C)−T_(IOLE) supplies all of the torque if inthe hybrid mode. This motor torque signal is transmitted to block 102.The power desired by the driver is then achieved instantly. If theaccelerator pedal is held constant at this point over time, then thetorque of the electric motor will decrease along a line of constantpower along line L₂ in FIG. 7, thus holding the power constant as thevehicle accelerates. This line L₂ represents the action of the feedbackloop as designed in FIG. 6 which includes blocks 102, 104, 106, 108 and110 (or 128 and 130), and 114 or 126. The vehicle will continue toaccelerate with motor torque decreasing along line L₂ until the point Cis reached along the constant power line L₂. This point is reached whenP_(EP) is iteratively reduced to zero and P_(C)=P_(IOl). It will beappreciated that at all times during this process, the engine alwaysoperates along the IOL.

The car then will maintain this speed until the position of acceleratorpedal is again changed. If the accelerator pedal is now reduced to theoriginal position, the net torque will be reduced to point D, and speedwill proceed back to point A along a constant power line L₄. Toaccomplish this, the electric motor/generator must supply a negativetorque to reach point D along line L₃. This happens instantly. As thenet torque and power proceeds along line L₄, the electricmotor/generator torque gradually approaches zero as the vehicle againbegins to cruise when the accelerator position returns to A_(CA). Notethat the deceleration maneuver returns energy to the battery systemdescribed above, and the acceleration maneuver takes energy from thebattery system while the engine continues to operate along the IOL.

It will be appreciated, therefore, that the throttle opening of theengine is set to provide the best efficiency for a given power along theIOL. The electric motor is used to force the engine to operate along theIOL and to provide correct transient response to the vehicle. Note thata large electric motor and a small engine is preferred, but theinvention can also employ a large engine and small electric motor withslower response. The CVT provides the correct speed and power setting asquickly as dynamics and motor capacity allow. The battery capacity isthen used to temporarily provide and absorb energy to allow the CVT tochange ratio without detrimental effects on performance. It will furtherbe appreciated that this is accomplished, in the preferred embodiment,by having the engine and the electric motor on the same shaft in thepreferred embodiment.

Based on the foregoing, it will be appreciated that the electric motorcan be used to supplement and control the gasoline or diesel engineduring both acceleration and deceleration of the vehicle, thus allowingthe engine to run at optimum efficiency across its entire speed bandwith generally a fixed throttle setting or in an un-throttled state soas to maximize engine efficiency. This is not possible in a conventionalcontinuously variable transmission system as discussed in FIG. 1.

Now, consider braking the vehicle with a brake command Bc in FIG. 6. Asthe brake pedal is depressed for a normal stop, switches SW1 and SW2 inFIG. 6 are set to the brake position. The braking level desired by thedriver is compared with the ideal regeneration line (IRL) at block 118at a given vehicle speed and transmission input speed S_(T) or motorspeed S_(M). The IRL is a line determined by testing the motor/generatorand battery system for the best efficiency for energy storage at eachspeed. After such testing procedure, an ideal line can be selected toconnect all the best efficiency points yielding the IRL.

The brake command Bc (at 34 in FIG. 6) represents a desired torque atthe drive shaft or wheels of the car. At block 122 the torque command isdivided by the ratio R to obtain the equivalent torque at the CVT input124. This input is compared with the torque along the IRL at the speedof the motor S_(M) at this instant. The error is used to command

 through the gain block 120 and filter block 112. The ratio R of thetransmission will change to seek the IRL via the feedback control systemof blocks 102, 104, 106, 112, 116, 118 and 120. It is understood thatthis control system becomes ineffective when the ratio reaches itsphysical limits Rmin or Rmax.

The desired torque at the output of block 122 is sent to block 100 tocompute the motor torque necessary to achieve the desired braking torqueat the driveshaft and consequently the wheels of the car. Initially thetorque at the motor is T_(C)/R since R is zero at the start of themaneuver.

From the foregoing, it should be apparent that there is a need forsystems and methods for efficiently and effectively controlling the rateof change of ratio

, not simply the ratio, in a CVT. Furthermore, because a CVT is adrivetrain component and various load conditions can cause the CVT toslip, various approaches have been taken to control CVT pressure andminimize slip. However, conventional control mechanisms are mechanicallybased, using valves, orifices, and the like, and are conservativelydesigned for high pressure conditions which leads to lower efficiencyand durability. Accordingly, there is also a need for a pressure controlmechanism and method that controls the pressure in a CVT to prevent slipunder all driver input conditions.

BRIEF SUMMARY OF THE INVENTION

Accordingly, the present invention pertains to systems and methods forefficiently and effectively controlling the rate of change of ratio, notsimply the ratio, in a CVT. By controlling the rate of change of ratio,the acceleration or deceleration of a vehicle can be controlled in anefficient manner. Furthermore, the rate of change of ratio can becontrolled by controlling the clamping pressure of the pulleys and/ordifferential pressure between the pulleys with minimal slip.

The present invention recognizes that the overall behavior of a CVT isdependent upon a number of variables, such as clamping pressure,differential pressure between pulleys, oil temperature, input shaftspeed, and torque. In view of those variables that affect CVT behavior,the present comprises systems and methods for mapping performancevariables to an output value, such as differential pressure needed toachieve a desired rate of change of ratio.

By way of example, and not of limitation, the present inventioncomprises a computerized controller having programming that includes analgorithm, set of algorithms, map or set of maps, that relate inputcriteria such as existing ratio, torque, speed, and clamping pressure tothe level of differential pressure needed to achieve a rate of change ofratio. Once a rate of change of ratio is selected, the clamping ordifferential pressure is controlled to achieve that rate of change ofratio.

By way of further example, the invention comprises a method andapparatus for providing for optimal control of the primary and secondarypressure of a CVT in order to achieve an ideal commanded clampingpressure due to the input torque command and the commanded rate ofchange of ratio (or shift velocity), by using previous knowledge of theoperational characteristics of the CVT.

An aspect of the invention, therefore, is to control the clampingpressures of the primary and secondary pulleys in a CVT as necessary toachieve a desired rate of change of ratio.

Another aspect of the invention is to control the differential pressurein a CVT as necessary to achieve a desired rate of change of ratio.

Another aspect of the invention is to determine the differentialpressure in a CVT that corresponds to a particular rate of change ofratio.

A further aspect of the invention is to map operational characteristicsto a desired differential pressure in a CVT. Those characteristicsinclude clamping pressure, speed, torque, current differential pressure,current ratio, oil temperature, etc.

Another aspect of the invention is an algorithm for determiningdifferential pressure in a CVT for producing a desired rate of change ofratio.

Another aspect of the invention comprises empirical data which is usedfor the above-described mapping and algorithm.

Another aspect of the invention is to provide an apparatus forcontrolling the rate of change of ratio in a continuously variabletransmission (CVT). In one embodiment, the apparatus comprises acontroller and means associated with the controller for mapping at leastone operational characteristic of the CVT to at least one controlcharacteristic. The operational characteristic can, for example,comprise CVT clamping pressure, input shaft speed, torque, differentialpressure between pulleys, ratio, and oil temperature.

Another aspect of the invention is to provide a hybrid electric vehiclewith dynamic control of the rate of change of ratio in the CVT. In oneembodiment, the vehicle comprises an internal combustion engine coupledto the CVT, an electric motor coupled to the output of the internalcombustion engine, and a computerized system controller configured tooperate said motor simultaneously with said engine and apply positive ornegative motor torque to said engine output to maintain engine poweroutput substantially along a predetermined operating line, wherein thecontroller is configured to control rate of change of ratio of said CVTusing said means for mapping, and wherein the system controller controlsthe rate of change of ratio of the CVT and said motor torque to varyacceleration or deceleration of said vehicle.

Another aspect of the invention is to provide an apparatus forcontrolling the operation of a continuously variable transmission (CVT).In one embodiment, the apparatus comprises a programmable controller andprogramming associated with said controller for mapping at least oneoperational characteristic of the CVT to at least one controlcharacteristic of the CVT. The operational characteristic can, forexample, comprise CVT clamping pressure, input shaft speed, torque,differential pressure between pulleys, ratio, and oil temperature. Inanother embodiment, the apparatus comprises a controller and analgorithm or map associated with the controller, wherein the algorithmor map determines differential pressure level between pulleys in the CVTfor achieving a desired rate of change in ratio in the CVT.

The invention also comprises a method and apparatus for controlling theoperation of a continuously variable transmission (CVT) having two pairsof conical disks mutually coupled by a chain or belt as a powertransmission element, in which at least one disk of each pair is coupledto a hydraulic actuator. By way of example, and not of limitation, inone embodiment, the invention comprises two hydraulic pumps driven bytwo servomotors, and a control processor with programming forcontrolling both the primary and secondary pressures simultaneously. Theinvention is applicable to any CVT, which allows the control of theprimary and secondary pressures by one way or another. The invention canalso be used with CVTs where only one pressure is fully controllable.

Accordingly, another aspect of the invention is a method comprisingcontrolling the primary and secondary pressure of a CVT to achieve anideal commanded clamping pressure for the input torque command andcommanded ratio rate or shift velocity based on a mapping of empiricaldata relating pressures, ratio rate, and torque input. In oneembodiment, this is achieved by mapping the relationship between primaryand secondary pressures of the CVT and rate of change of ratio totransmit a given amount of torque, and controlling the primary andsecond pressure of the CVT to achieve an optimized clamping pressure forcommanded torque and ratio rate based on said mapping. In anotherembodiment, this is achieved by determining an equilibrium ratio map ofa CVT to be controlled, determining a pressure relationship between theratio rate of the CVT and the distance between the point correspondingto the current states of the CVT and the projection of this point ontosaid equilibrium ratio map, and using the equilibrium ratio map and saidpressure relationship, controlling the primary and secondary pressuresof the CVT to control the ratio rate and/or ratio and clamping pressureof the CVT.

Another aspect of the invention is an apparatus for optimizing theoperation of a CVT. In one embodiment, the apparatus comprises a controlcomputer and programming associated with the control computer forcarrying out the operations of controlling the primary and secondarypressure of a CVT to achieve a ideal commanded clamping pressure due tothe input torque command and commanded ratio rate or shift velocitybased on a mapping of empirical data relating pressure, ratio rate, andtorque. In another embodiment, the apparatus comprises a controlcomputer and programming associated with said control computer foraccessing a map of the relationship between pressure of a CVT and rateof change of ratio to transmit a given amount of torque, and forcontrolling the primary and second pressure of the CVT to achieve anoptimized clamping pressure for commanded torque and ratio rate based onsaid map. In a still further embodiment, the apparatus comprises acontrol computer and programming associated with said control computerfor carrying out the operations of controlling the primary and secondarypressures of the CVT to control the ratio rate and/or ratio and clampingpressure of the CVT based on an equilibrium ratio map of the CVT and thepressure relationship between the ratio rate of the CVT and the distancebetween the point corresponding to the current states of the CVT and theprojection of this point onto the equilibrium ratio map.

Further aspects of the invention will be brought out in the followingportions of the specification, wherein the detailed description is forthe purpose of fully disclosing preferred embodiments of the inventionwithout placing limitations thereon.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

The invention will be more fully understood by reference to thefollowing drawings which are for illustrative purposes only:

FIG. 1 is a functional block diagram of a conventional vehicle with apowertrain employing a continuously variable or multi-speed automatictransmission known in the art.

FIG. 2 is a graph showing the torque-speed efficiency map of a typicalcombustion engine showing maximum torque at wide open throttle (WOT) andan ideal operating line (IOL) which produces the best efficiency andminimum emissions for a given power of the engine shown in FIG. 1.

FIG. 3 is a graph showing the practical operating line (POL) requiredfor the conventional vehicle shown in FIG. 1 compared with the idealoperating line (IOL).

FIG. 4 is a functional block diagram of a control apparatus in aparallel hybrid configuration having a continuously variabletransmission in the drive train illustrative of what is in the art.

FIG. 5 is a functional block diagram of an alternative embodiment of thecontrol apparatus shown in FIG. 4 in a conventional series hybridconfiguration having a continuously variable or automatic transmissionin the drive train.

FIG. 6 is a flow diagram showing a control method for a hybrid vehiclehaving a continuously variable transmission as seen in the art.

FIG. 7 is a graph showing engine and electric motor/generator torque asa function of engine and transmission speed, as well as the operationalboundary for acceleration and a typical acceleration/deceleration cyclefor the apparatus shown in FIG. 4.

FIG. 8 is a schematic diagram of an embodiment of hydraulic pressureservo control system for controlling a CVT according to the presentinvention.

FIG. 9 is a block diagram of an embodiment of an apparatus in accordancewith the present invention for controlling the pressure in a CVT bymeans of the control system shown in FIG. 8.

FIG. 10 is a schematic diagram of a vehicle control infrastructureaccording to the present invention.

FIG. 11 is a simplified schematic of a CVT powertrain.

FIG. 12 is a diagram showing the basic geometry of a CVT powertraincorresponding to FIG. 11.

FIG. 13 is a series of graphs illustrating errors introduced bysecond-degree approximation in CVT dynamic equations.

FIG. 14 is diagram illustrating CVT chain misalignment for differentgeometric ratios when one sheave is moveable and the other is fixed.

FIG. 15 is a graph showing the relationship between chain misalignmentangle and ratio for fixed sheaves.

FIG. 16 is a diagram illustrating tensile forces in a positive torquecondition in a v-belt drive CVT.

FIG. 17 is a series of diagrams illustrating forces on an infinitesimalportion of a chain and the contact forces on a sheave.

FIG. 18 is a diagram illustrating tensile forces in a negative torquecondition in a v-belt drive CVT.

FIG. 19 is a graph illustrating pulley thrust at slip limit showing thatclamping force as a function of ratio is non-monotonic.

FIG. 20 is theoretical equilibrium map according to the presentinvention.

FIG. 21 is a series of diagrams illustrating the influence of cylinderdesign on clamping pressure.

FIG. 22 is a schematic diagram illustrating pump rotational directionsand flow orientations in a servo control mechanism according to thepresent invention corresponding to a positive P speed and a negative R.speed.

FIG. 23 is a chart showing experimental equilibrium map data for a servocontrol mechanism according to the present invention.

FIG. 24 is a graph showing illustrating experimental equilibrium datapoints from FIG. 23 and the theoretical equilibrium map from FIG. 20.

FIG. 25 is a graph showing equilibrium data points on the torqueratio-thrust ratio plane for different transmission ratios along withtheoretical results for the same transmission.

FIG. 26 is a series of graphs showing an approximation of experimentaldata points into a plane.

FIG. 27 is a flow diagram of an embodiment of a pressure-based controlalgorithm according to the present invention.

FIG. 28 is a series of graphs illustrating test results for pressurebased control testing.

FIG. 29 is a schematic diagram of an independent servo pump controlsystem according to the present invention.

FIG. 30 is a series of graphs illustrating macro slip.

DETAILED DESCRIPTION OF THE INVENTION

The present invention generally comprises a method and system forcontrolling the rate of change of ratio in a CVT. In the preferredembodiment, the invention employs an algorithm, set of algorithms, mapor set of maps, that relate input criteria such as existing ratio,torque, speed, and clamping pressure to the level of differentialpressure needed to achieve a rate of desired rate of change of ratio. Inother words, once the desired rate of change of ratio is determined,this mapping can be used in conjunction with the dynamic equations forcontrolling rate of change of ratio to achieve the desired rate ofchange. The present invention also comprises a method and system forproviding optimal control of the primary and secondary pressure of acontinuously variable transmission (CVT), in order to achieve an idealcommanded clamping pressure due to the input torque command and thecommanded rate of change of ratio (or shift velocity), by using previousknowledge of the operational characteristics of the CVT.

Referring to FIG. 8, an embodiment of a CVT physical control systemaccording to the present invention is shown. In the general embodimentschematically shown in FIG. 8, the control system 100 comprises ahydraulic pressure pump 102, a hydraulic shift pump 104, a pressureservomotor 106, a shift servo motor 108, a control valve 110, and ahydraulic fluid tank 112. As can be seen, the control system isfluidically coupled to the primary pulley 114 and the secondary pulley116. This control hardware can differ from that shown in FIG. 8, but inany case, it should allow for the control of both the primary andsecondary pressures simultaneously.

More particularly, the invention comprises an apparatus and method forcontrolling a CVT having at least a pair of pulleys 114, 116 each ofwhich has a pair of conical disks 118 a, 118 b and 120 a, 120 b,respectively, mutually coupled by a chain or belt 122 as the powertransmission element, in which at least one disk of each pair is coupledto a hydraulic actuator 124, 126, respectively, as shown in FIG. 8. Theinvention is applicable to any CVT which allows the control of theprimary and secondary pressures by one way or another. In the case whereonly one pressure is fully controllable, the control method describedbelow can still be used.

In a preferred embodiment of the invention, the primary and secondarypressures of the CVT are controlled so as to achieve an ideal commandedclamping pressure due to the input torque command and the commandedratio rate (or shift velocity), by using previous knowledge of theoperational characteristics of the CVT (e.g., obtained empirically).Referring also to FIG. 9, this will be accomplished using a computerizedCVT pressures controller 200 according to the following steps:

1. First, determine the equilibrium ratio map 202 of the CVT that isbeing controlled. This map can be considered a complex function of theprimary pressure (P₁), the secondary pressure (P₂), the torque input(T_(in)), the input speed and/or any combination of these variables,that returns a geometric ratio (R) corresponding to the equilibriumstate that the CVT will take under these conditions. This can beexpressed in terms of the following function:ƒ(P ₁ P ₂ ,T _(in),InputSpeed)=(ratio)_(equilibrium)

2. Verify that there exists some relationship(s) linking the ratio rate(rate of change of the geometric ratio) and the distance between thepoint corresponding to the current states 204 of the CVT (P₁, P₂,T_(in), InputSpeed, ratio) and the projection of this point onto theequilibrium map previously determined. This relationship can beconsidered as one more dimension added to the previously describedequilibrium map.

3. Using these previously determined equilibrium map andrelationship(s), the primary P₁ and secondary P₂ pressures of the CVTare simultaneously controlled to achieve an optimal control for the CVT.This optimal control allows a direct control of ratio rate and/or ratioand clamping pressure. Given a ratio rate strategic command 206 and atorque input command 208, the controller uses the previously defined mapand relationships and some calculations (for input torque and minimumnecessary clamping pressure) to determine the optimal pressures 210 tocontrol in both the primary and secondary hydraulic actuators in orderto achieve the commands and draw a minimum of power. These optimalpressures will prevent CVT slip. The invention has also the advantage ofbeing able to include limits on both pressures as well as limits on theshift rate onto these multidimensional maps.

It will be appreciated that the foregoing steps are implemented insoftware, firmware or the like associated with the controller 200. Inturn, controller 200 provides one or more output signals to controlpressure pump 102, shift pump 104, pressure motor 106, shift motor 108,control valve 110, and any other elements of the physical controller 100as necessary. It will also be appreciated that a direct extension of theforegoing would be to employ a learning controller, such as a neuralnetwork or the like, which would learn, build and correct theequilibrium map and the ratio rate map as the CVT is used and controlledto compensate for oil temperature and conditions as well as changes inthe internal components. In this way, an initial mapping could be usedand updated based on actual operational conditions of the CVT in thefield.

Another aspect of the invention is the control valve 110 shown in FIG. 8that bypasses the pressure pump 102 driven by the pressure motor 106.This valve is open at low pressure to permit a sufficient leak andcloses as the secondary pressure rises in order to limit the leak flow.This valve can be controlled by controller 200 or simply by thesecondary pressure itself fighting against a spring. This leak valvemakes the control system more stable and thus helps for the control ofthe secondary pressure. The same concept may be used in the shift servopump 104 for control of the primary pressure.

It will be appreciated that the invention has several additionalaspects, including but not limited to:

1. Design of the pulleys hydraulic piston: the ratio of the active areaof the primary to the secondary hydraulic actuators can be optimizedfrom the information provided by the equilibrium map in order tominimize the energy usage of the hydraulic control system. For example,considering the configuration of FIG. 8, noting that the ratio of thrust(Q₁/Q₂) is mostly in a range around 1.0, both areas should be designedto be equal so that the shift motor does not have to be used too much.

2. Selection of servomotors and pumps: from the previous aspect of theinvention, and its general use, for optimal control of a CVT the maximumpower, the flow of the pumps and the maximum torque and speed of theservomotors can be measured or calculated in order to select the mostsuitable components (in terms of cost, size, quality, effectiveness,etc) for the control hardware.

Accordingly, it will be appreciated that the present invention optimizesthe control of a CVT to prevent slip under all conditions of driverinputs. By obtaining empirical data from the CVT that relates thepressure required to transmit a given torque and the ratio that resultsfrom that pressure, a formula can be derived that characterizes thepressure required to safely cause a change in ratio. That formula canthen be used in the programming associated with a computer to controlthe operation of the CVT. The goal is to control the CVT under alldriver input conditions without underloading or overloading the CVT. Thecontroller will sense the power/torque commanded by the driver andessentially tell the CVT to shift a rate of change of ratio and transmitthe desired torque.

Referring now to FIG. 10, CVT pressures controller 200 would typicallybe implemented as a component in an overall vehicle control systemcomprising a power control module (PCM) 240, which functions as astrategy controller, and CVT controller (CVTC) 300, which functions as alow-level controller. The functions of the CVT pressures controllerwould be subsumed by CVTC 300 in this configuration. The controlelectronics would preferably comprise PC 104 microcomputers, an industrystandard for microcontroller platforms, or other microcomputers orprogrammed data processors. Preferably, PCM 250 and CVTC 300 communicateover a digital control area network (CAN) 3500 rather than analogchannels. Digital communication ensures reliability and improves datatransfer precision. PCM 250 sends strategic commands to the CVTC 300depending on the driver's desire and the hybrid control strategy. Inturn, CVTC 300 then controls the CVT by carrying out the following maintasks:

1. Uses strategic commands from the PCM 250 to determine set points forthe clamping pressure and ratio.

2. Measures CVT states (pressures, ratio, speeds).

3. Calculates the transmissible torque from the CVT states.

4. Computes both ratio and pressure close loop regulations.

5. Sends commands to the CVT servomotors to operate closed loop control.

6. Sends commands to the powertrain (electric motor and/or engine)depending on the PCM strategic commands and the transmissible torque.

While the inventive servo control mechanism can be used with aconventional CVT, it is preferable to modify the pulley configuration tofunction with the inventive servo control mechanism described above.More particularly, to be specifically adapted for use with the inventiveservo hydraulic control system, the primary and secondary pulleys arepreferably designed to be identical. We will refer to this modified CVTas a Servo Controlled CVT, or SC-CVT. Use of identical primary andsecondary pulleys simplifies the transmission and also reducesmanufacturing and assembling costs. Additional advantages of usingidentical pulleys (so A₁/A₂=1) will be discussed in more detail later.

In our prototype SC-CVT, the gear pumps were selected to have a verysmall displacement (1.07 cc/rev) and rating of 3000 PSI. Both pumps weremounted inside the CVT case and connected to servomotors through holesin the case. This constituted the servo-pump system. Permanent magnetbrushless DC motors were selected to drive the gear pumps. Brushlessservomotors, due to the use of permanent magnets, are capable of highertorque to inertia ratios and power to size ratios than regular inductionmotors. Due to the cost of earth magnets, they are typically reservedfor high performance applications. The servomotors were selected to havea very fast response with a mechanical time constant of 3.8 ms, a lowcogging torque and a maximum theoretical acceleration of more than55,000 rad/sec². Brushless servo amplifiers were selected to drive thedirect current (DC) servomotors. The amplifiers represent the electronicpower converter that drives the motor according to the controllerreference signals. The amplifiers basically translate low-energyreference signals from the controller into high-energy signals (motorvoltage and current). In the case of brushless motors, the amplifier isalso responsible for the proper commutation of the magnetic field. AModel B30A40 from Advanced Motion Controls, for example, is suitable forinterfacing with digital controllers and can be used in open loop,current close loop or speed close loop mode. For this application, theamplifiers are used in a current close loop Configuration, whichcorresponds to controlling the torque of the DC motors.

The prototype CVTC was based on a Micro/sys SBC 1486, PC 104 type,microcontroller board, a E-CAN board to ensure network communication, aMicro/sys MPC 550 input/output board and a custom-made signalconditioning board. The control code was written in C++ and loadedthrough a serial port into the microcontroller. The SC-CVT was equippedwith two pressure sensors, two speed sensors and a linear potentiometerfor position measurement. Therefore, pressures and speeds of the primaryand secondary pulleys could be measured. Proximity switches (inductivespeed sensors with amplifiers) were used to sense pulley speed, and atrigger wheel was mounted on both fixed sheaves. These speed sensorsoutput a square signal interpreted by timer/counters in the MPC 550. Theposition sensor was connected to the primary pulley movable sheave andits output was used to calculate the CVT geometric ratio. It will beappreciated that ratio can also be obtained using the speed signals butposition sensing offers the advantage of measuring ratio even at zerospeed.

Table 1 depicts the main parameters of the above-described prototypeSC-CVT. It will be appreciated that these parameters are given by way ofexample only.

Our prototype SC-CVT had a design capacity of 700 Nm. The electricmotor, through its reduction gearing, was capable of producing 540 Nm,and the engine was capable of producing up to 190 Nm. Although thetheoretical maximum torque of the powertrain was 730 Nm, because theelectric motor torque depends on the voltage of the battery pack, andbecause the maximum torque of the engine and electric motor do not occurat the same rotational speed, the maximum torque reached by thispowertrain was 650 Nm. Moreover the engine could not be operated at lowspeed because it was directly coupled to the input pulley through anautomotive clutch.

To verify the torque capacity of the SC-CVT, acceleration runs wereperformed with the SC-CVT installed in a 2000 Chevrolet Suburban thatwas converted into a parallel hybrid-electric vehicle, and powered by a150 kW electric motor and a Saturn 2.2 liter internal combustion engine.The tests were for a 0 to 60 mph acceleration and a 60 to 0 mphdeceleration range. The SC-CVT proved its torque capacity by performingthis test without breaking or even slipping the chain. The decelerationobserved was faster than the acceleration because the mechanical brakeswere applied simultaneously on top of the 300 Nm of regenerative torquecapability of the electric motor. The final time was 10.9 seconds forthe 0 to 60 mph and less than 9 seconds for the 60 to 0. These resultswere very promising for the Suburban, considering that this truck weighsmore than 3000 kg due to the lead acid battery pack on-board to powerthe electric motor.

A series of driving tests was conducted with the Suburban, to prove theSC-CVT concept and demonstrate the controllability of the transmissionunder driving conditions. The truck was also driven on standard drivingcycles in order to verify the vehicle drivability and the SC-CVTperformed satisfactorily.

One of the design goals of the SC-CVT was to exhibit reliable operationfor the entire lifetime of a commercial vehicle; however, significantwear was observed on the chain and pulleys after less than 50 hours ofoperation. Such severe wear indicated macro slip of the chain on thepulleys. Macro slip occurs when the clamping forces, applied by thepulleys on the chain, become too low to transmit the torque applied byeither the input or output pulley. To avoid further macro slipoccurrence, a 10% safety factor was added to the clamping pressure map,and no additional wear was observed. This experience illustrates themajor failure of CVTs, and reinforces the need of a close loopregulation on the clamping pressure as well as a complete knowledge ofthe limitation of the particular CVT in use. This last factor wascertainly the one to blame in this case since this transmission was thefirst of its kind ever made.

From the foregoing, it will be appreciated that in order to control theprimary and second pressures to achieve a desired rate of change ofratio, certain information regarding the CVT is required to develop theequilibrium maps and other control parameters. A more detaileddiscussion of the operational theory and implementation follows.

CVT Dynamic Equations

The dynamic ratio of a CVT is defined as the ratio of the input speeddivided by the output speed. It can be measured only when both speedsare greater than zero and becomes more accurate as speed increases.

$\begin{matrix}{i = \frac{\omega_{1}}{\omega_{2}}} & (1)\end{matrix}$

By taking the derivative of (1):{dot over (ω)}₁ =i·{dot over (ω)} ₂+ω₂ ·{dot over (i)}  (2)

The simplified schematic presented in FIG. 11 is used to derive thedynamic equations. The chain 400 is considered massless, the chain slipis assumed to be zero and the inertia of the CVT primary 402 andsecondary 404 pulleys are taken into account in the powertrain andvehicle inertias (Ip and Ic, respectively).

From the dynamic ratio, the relation between input and output torque isas follows, when neglecting the chain losses:

$\begin{matrix}{i = \frac{T_{out}}{T_{in}}} & (3)\end{matrix}$

Using Newton's law at the primary and secondary pulleys:{dot over (ω)}₁ ·I _(p) =T _(P) −T _(in)  (4){dot over (ω)}₂ ·I _(c) =T _(out) −T _(R)  (5)

Substituting (3) into (5):{dot over (ω)}₂ ·I _(c) =i·T _(in) −T _(R)  (6)

then, using (4) and (2) in (6):{dot over (ω)}₂ ·I _(c) =i·T _(P) −i ²·{dot over (ω)}₂ ·I _(p) −i·I _(p)·{dot over (i)}·ω ₂ −T _(R)  (7)

Finally, substituting (1) into (7) and solving for the vehicleacceleration:

$\begin{matrix}{{\overset{.}{\omega}}_{2} = \frac{{i \cdot T_{p}} - {I_{p} \cdot \overset{.}{i} \cdot \omega_{1}} - T_{R}}{I_{c} + {i^{2} \cdot I_{p}}}} & (8)\end{matrix}$

Note that the second term in the numerator depends on the rate of changeof ratio ({dot over (i)}). This translates into an acceleration of thevehicle due to the shift rate of the transmission. Up-shifting causes apositive acceleration, whereas down-shifting causes a deceleration ofthe vehicle. This can sound surprising at first but it comes from thetransfer of kinetic energy from the powertrain inertia to the vehicleinertia, resulting in negative acceleration. This equation is notspecific to CVTs but can be applied to any transmission. However, in thecase of discrete gear transmissions, the powertrain has to be decoupledfrom the transmission in order to shift, causing a much more complexphenomenon and making equation (8) not applicable. In CVTs, the rate ofchange of ratio is usually limited to reduce the effect of this term onthe vehicle drivability. In the case of parallel hybrids, theacceleration induced by the rate of change of ratio can be compensatedby using the electric traction motor to supply a compensating torque. Todo this effectively, the motor torque needs to be substantially largerthan the engine IOL torque, and the compensation torque depends on theshifting speed desired.

CVT Geometry

The basic geometry of a CVT is presented in FIG. 12. The geometric ratiocan be calculated from the running radii R₁ and R₂.

$\begin{matrix}{r = \frac{R_{2}}{R_{1}}} & (9)\end{matrix}$

The geometric ratio is equivalent to the dynamic ratio when the chainslip is null. This leads to the definition of slip:

$\begin{matrix}{S = \frac{i - r}{i}} & (10)\end{matrix}$

The slip depends on the amount of torque transmitted through thetransmission, the clamping forces applied and the geometric ratio.Micro-slip is normal and can get up to 6% with a van Doorne push belt.The GCI chain is supposed to limit micro-slip to less than 4%.

If the chain is assumed to be inextensible, the chain length can be usedto constrain the relationship between running radii (R₁ and R₂). Theangle δ is determined by the geometric ratio r. δ will be consideredpositive in the orientation drawn in FIG. 12 and negative when R₁ isgreater than R₂. The resulting geometric relationship for the chainlength is given below:

$\begin{matrix}{L = {{2 \cdot \delta \cdot \left( {R_{2} - R_{1}} \right)} + {\pi \cdot \left( {R_{2} + R_{1}} \right)} + {{2 \cdot {CD} \cdot \cos}\;\delta}}} & (11) \\{\delta = {\arcsin\left( \frac{R_{2} - R_{1}}{CD} \right)}} & (12)\end{matrix}$

Using second-degree Taylor series expansions of cosine and sine,equations (11) and (12) become:

$\begin{matrix}{L = {{2 \cdot \delta \cdot \left( {R_{2} - R_{1}} \right)} + {\pi \cdot \left( {R_{2} + R_{1}} \right)} + {2 \cdot {CD}} - {{CD} \cdot \delta^{2}}}} & (13) \\{\delta = \frac{R_{2} - R_{1}}{CD}} & (14)\end{matrix}$

Substituting (14) into (13), the chain length constraint equationbecomes:

$\begin{matrix}{L = {\frac{\left( {R_{2} - R_{1}} \right)^{2}}{CD} + {\pi \cdot \left( {R_{2} - R_{1}} \right)} + {2 \cdot {CD}}}} & (15)\end{matrix}$

Finally, solving the quadratic equation for either running radii:

$\begin{matrix}{R_{2} = {R_{1} - {\frac{\pi}{2} \cdot {CD}} + \sqrt{\frac{{CD}^{2} \cdot \pi^{2}}{4} - {2 \cdot \pi \cdot {CD} \cdot R_{1}} - {2 \cdot {CD}^{2}} + {{CD} \cdot L}}}} & (16) \\{R_{1} = {R_{2} - {\frac{\pi}{2} \cdot {CD}} + \sqrt{\frac{{CD}^{2} \cdot \pi^{2}}{4} - {2 \cdot \pi \cdot {CD} \cdot R_{2}} - {2 \cdot {CD}^{2}} + {{CD} \cdot L}}}} & (17)\end{matrix}$

Now either running radius can be measured to determine the other one andthen the geometric ratio r. Because the sheaves are conical and thechain width is invariant and known, there is a linear relation betweenthe lateral position of a movable sheave and the running radius of thecorresponding pulley. In the configuration shown in FIG. 8, the primarypulley movable sheave position is measured in order to determine R₁,then using equations (16) and (9), the geometric ratio r is obtained.

Equations (16) and (17) have been derived using a simplified model andtherefore they do not constitute an exact result. The error caused fromthe second-degree approximation of equation (11) and (12) resulting insimplified constraint (15) has been verified to be reasonably small (seeFIG. 13).

Chain Misalignment

Because only one sheave in each pulley is able to move in axialdirection (in and out) while the other stays fixed, and because thepulleys are cones whose apexes lie on the centerline of the sheaves, thechain cannot run in a plane perpendicular to the pulley axes at anygeometric ratio. FIG. 14 illustrates this deviation. To prevent thisdeviation, it is possible to make the cone-form of the v-sheave slightlyand outwardly spherical or crowned. This would increase manufacturingcosts and require that a high accuracy be maintained during the completeCVT life. However the belt and chain can endure a small misalignment. Inthe case of the present design, if the fixed sheaves are wellpositioned, the misalignment angle can be kept below 0.07° as shown inFIG. 15.

Clamping Map

In order to calculate clamping forces, it is necessary to understand thetorque transmission mechanism in a CVT. FIG. 16 shows the forcedistribution in a v-belt drive CVT. The vectors drawn perpendicular tothe transmission element represent the magnitude of the tension forceacting on the chain at a particular point. For the case shown the torqueinput is positive, which means that the torque is applied in thedirection of rotation. This also results in F₁ being greater than F₂.

The contacting arcs γ₁ and γ₂ depend on the geometric ratio r and aregiven by the following equations:γ₁=π−2·δ  (18)γ₂=π−2·δ  (19)

Combining (18) and (19) leads to:γ₂−γ₁=4·δ  (20)

Six different regions can be distinguished along the chain, startingfrom the primary pulley chain entrance:

(1) From point A to point B: angle ν₁ is the primary pulley rest arc,the tension force is constant and equal to F₁.

(2) From point B to point C: angle α₁ is the primary pulley active arc,the tension force decreases gradually from F₁ to F₂.

(3) From point C to point D: slack side of the chain, the force isconstant and equal to F₂

(4) From point D to point E: angle ν₂ is the secondary pulley rest arc,the tension force is constant and equal to F₂

(5) From point E to point F: angle α₂ is the primary pulley active arc,the tension force increases gradually from F₂ to F₁.

(6) From point F to point A: tight side of the chain, the force isconstant and equal to F₁.

The Eytelwein formula describes the forces distribution in a v-groovebelt system:

$\begin{matrix}{{F(\varphi)} = {F_{2} \cdot {\mathbb{e}}^{\frac{\mu \cdot \varphi}{\sin\;\beta}}}} & (21)\end{matrix}$

Here, β is the half wedge angle of the sheaves (11° in the SC-CVT), isan angle in the active arc α, (0≦φ≦α), and μ is the coefficient offriction (0.09 for steel belt and chain CVTs). The force distribution onboth pulleys must satisfy the Eytelwein formula. Since μ and β are thesame on both pulleys, the force distribution follows the same profile inthe active arc when the force decreases from F₁ to F₂ or increases fromF₂ to F₁. Therefore, α₁=α₂=α.

The slip limit is reached when the contacting arc γ is used in totalityto transmit the torque, which means that the rest arc ν is equal to 0.Slip occurs when the contacting arc is smaller than the active arcneeded to transmit the amount of torque applied. Since the active arc isthe same in both pulleys, the first side to slip is always the pulleywith the smallest contacting arc and thereby the smallest runningradius. Therefore to prevent the chain from slipping, the chain has tobe slightly over-clamped causing both pulleys to show a rest arc v atall times.

We now examine the clamping forces and the way they act between thechain and pulleys. FIG. 17 shows an infinitesimal portion of chain oflength and the contact forces on a sheave. The equilibrium of forces onthe infinitesimal portion of the chain results in:

$\begin{matrix}{{{dF}_{r} = {{2 \cdot F \cdot {\sin\left( \frac{d\;\varphi}{2} \right)}} \approx {{F \cdot d}\;\varphi}}}{and}} & (22) \\{{dN} = \frac{{dF}_{r}}{{2 \cdot \sin}\;\beta}} & (23)\end{matrix}$

At the contact point,dN _(x) =dN·cos β  (24)

Then, using equations (22) through (24),

$\begin{matrix}{{Dn}_{X} = {{\frac{F}{{2 \cdot \tan}\;\beta} \cdot d}\;\varphi}} & (25)\end{matrix}$

Now, by integrating dN_(x) over the contacting arc:

$\begin{matrix}{F_{\alpha\; x} = {\int_{\gamma}{{\frac{f(\varphi)}{{2 \cdot \tan}\;\beta} \cdot d}\;\varphi}}} & (26)\end{matrix}$

is known from FIG. 16 and equation (21). Hence,

$\begin{matrix}{F_{\alpha\; x_{1,2}} = {{\int_{0}^{\alpha}{{\frac{F_{2}}{{2 \cdot \tan}\;\beta} \cdot {\mathbb{e}}^{\frac{\mu \cdot \varphi}{\sin\;\beta}} \cdot d}\;\varphi}} + {\int_{0}^{v_{1,2}}{{\frac{F_{1,2}}{{2 \cdot \tan}\mspace{11mu}\beta} \cdot d}\;\varphi}}}} & (27)\end{matrix}$

Indices 1, 2 in this formula refer respectively to the primary andsecondary pulleys. By integrating equation (27), the clamping forces inboth pulleys can be calculated.

$\begin{matrix}{F_{\alpha\; x_{1,2}} = {{\frac{{F_{2} \cdot \cos}\;\beta}{2 \cdot \mu} \cdot \left( {{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \right)} + {\frac{F_{1,2}}{{2 \cdot \tan}\mspace{11mu}\beta} \cdot v_{1,2}}}} & (28)\end{matrix}$

The equilibrium of forces on the input sheave translates to:

$\begin{matrix}{\frac{T_{in}}{R_{1}} = {F_{1} - F_{2}}} & (29)\end{matrix}$

Also from the Eytelwein formula, when:

$\begin{matrix}{\frac{F_{1}}{F_{2}} = {\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}}} & (30)\end{matrix}$

Solving (29) and (30) for the forces F₁ and F₂:

$\begin{matrix}{{F_{1} = {\frac{T_{in}}{R_{1}}\left( \frac{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\;\beta}}}{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \right)}}{and}} & (31) \\{F_{2} = {\frac{T_{in}}{R_{1}}\left( \frac{1}{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \right)}} & (32)\end{matrix}$

Substituting (31) and (32) into (28), leads to the general equations forthe clamping forces for positive torque:

$\begin{matrix}{{F_{\alpha\; x_{1}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}}}{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{\gamma_{1} - \alpha}{{2 \cdot \tan}\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}}{and}} & (33) \\{F_{\alpha\; x_{2}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{1}{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{\gamma_{1} - \alpha}{{2 \cdot \tan}\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}} & (34)\end{matrix}$

In equations (33) and (34), the influence of the ratio is representedthrough R₁, and the active arcs (γ₁ and γ₂), and the equation is highlynonlinear. On the other hand, the relation between the clamping forcesand the torque input is linear. The differences (γ₁−α) in (33) and(γ₂−α) in (34) represent the over-clamping on the primary and secondarypulleys, respectively.

The negative torque case (when the powertrain is used to regeneratevehicle kinetic energy) cannot be assumed identical and symmetric to thepositive torque case, because the rest arc takes place at the entranceside of the pulleys. The negative torque input case is shown in FIG. 18.The slack side and tight side are now switched, so F₂ is applied alongthe arc AB (arc ν₁) and F₁ is applied along the arc DE (arc ν₂). Lookingat both FIG. 16 and FIG. 18, it can be observed that, at this ratio, thesecondary clamping force (Fax₂) would have to be higher for the negativetorque case than for the positive.

Following the same steps as for the positive torque case, the generalequations for the clamping forces for negative torque are obtained:

$\begin{matrix}{{F_{\alpha\; x_{1}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{1}{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{\gamma_{1} - \alpha}{{2 \cdot \tan}\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}}{and}} & (35) \\{F_{\alpha\; x_{2}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}}}{{\mathbb{e}}^{\frac{\mu \cdot \alpha}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{\gamma_{2} - \alpha}{{2 \cdot \tan}\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}} & (36)\end{matrix}$

Minimum Clamping Forces

To determine the minimum clamping forces at slip limit, equations (33)to (36) are used in the special case where the active arc α equals thesmallest contacting arc. Two cases must be considered. The cases are (a)the geometric ratio r is between low gear and 1:1 (r≧1), in which casethe primary pulley is the first one to slip; or (b) r is between 1:1 andoverdrive (r≦1), in which case the secondary pulley reaches the sliplimit first.

From equations (20), (33) to (36), and setting γ₁=α for r higher than1:1 and γ₂=α for r lower than 1:1, one obtains:

$\begin{matrix}{{{Positive}\mspace{14mu}{torque}}{r \geq {1\text{:}}}} & \; \\{{F_{\alpha\; x_{1\min}} = {\left( \frac{\cos\;\beta}{2 \cdot \mu} \right) \cdot \frac{T_{in}}{R_{1}}}}{and}} & (37) \\{{F_{\alpha\; x_{2\min}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{1}{{\mathbb{e}}^{\frac{\mu \cdot \gamma_{1}}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{2 \cdot \delta}{\tan\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}}{r \leq {1\text{:}}}} & (38) \\{{F_{\alpha\; x_{1\min}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{{\mathbb{e}}^{\frac{\mu \cdot \gamma_{2}}{\sin\mspace{11mu}\beta}}}{{\mathbb{e}}^{\frac{\mu \cdot \gamma_{2}}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{2 \cdot \delta}{\tan\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}}{and}} & (39) \\{{F_{\alpha\; x_{2\min}} = {\left( \frac{\cos\;\beta}{2 \cdot \mu} \right) \cdot \frac{T_{in}}{R_{1}}}}{{Negative}\mspace{14mu}{torque}}{r \geq {1\text{:}}}} & (40) \\{{F_{\alpha\; x_{1\min}} = {\left( \frac{\cos\;\beta}{2 \cdot \mu} \right) \cdot \frac{T_{in}}{R_{1}}}}{and}} & (41) \\{{F_{\alpha\; x_{2\min}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{{\mathbb{e}}^{\frac{\mu \cdot \gamma_{1}}{\sin\mspace{11mu}\beta}}}{{\mathbb{e}}^{\frac{\mu \cdot \gamma_{1}}{\sin\mspace{11mu}\beta}} - 1} \cdot \frac{2 \cdot \delta}{\tan\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}}{r \leq {1\text{:}}}} & (42) \\{{F_{{ax}_{1\;\min}} = {\left( {\frac{\cos\;\beta}{2 \cdot \mu} + {\frac{1}{{\mathbb{e}}^{\frac{\mu \cdot \gamma_{2}}{\sin\;\beta}} - 1} \cdot \frac{2 \cdot \delta}{\tan\;\beta}}} \right) \cdot \frac{T_{in}}{R_{1}}}}{and}} & (43) \\{F_{\alpha\; x_{2\min}} = {\left( \frac{\cos\;\beta}{2 \cdot \mu} \right) \cdot \frac{T_{in}}{R_{1}}}} & (44)\end{matrix}$

Equilibrium Map

Equations (37) to (44) define the axial forces to be applied to bothpulleys to prevent slip of the chain for any given input torque andratio. The smallest contacting arc of each of the two pulleys has beenconsidered as fully used to transmit torque. Thus, the CVT is at theslip limit all the time. Now, the properties of the CVT fluid are notperfectly known and can change with temperature. The torque input to thetransmission is usually not measured but evaluated based upon previouslydetermined engine and/or motor map; and, the force feedback iscalculated by measuring the pressure. Because of these facts, the CVTcannot be controlled based solely on equations (37) to (44). So somesafety margin must be added in order to prevent any macro slipoccurrence.

Due to the action/reaction principle, clamping forces applied at thesecondary result in forces at the primary. In general, the secondarypressure is controlled and referred to as the clamping pressure; but theprimary pressure could be used for that purpose as well. Onedisadvantage of controlling the primary pressure for clamping forces isthat, in the positive torque case, the clamping force as a function ofratio is non-monotonic (see FIG. 22) whereas the secondary clampingforce function is monotonic for both positive and negative torque.Secondary pressure is referred to as the CVT clamping pressure and isused for the feedback control of the transmissible torque through thetransmission. In order to keep the transmission ratio constant, theprimary pressure is used to balance the effort caused by the clampingpressure. Steady state is achieved when an equilibrium is establishedfor the torque input, the geometric ratio, the secondary clamping forceand the primary clamping force. This equilibrium involves fourvariables; the first two (Tin, r) are commands and the other two are theclamping forces needed to operate the transmission properly. In order tocalculate the equilibrium parameters for a given state, equations (33)and (34) are used for positive torque, and equations (35) and (36) fornegative torque.

In the case of positive or driving torque, equation (34) can be used todetermine the active arc a from the secondary clamping force, the torqueinput and the geometric ratio. Then the active arc is used in (33) withthe torque input and geometric ratio to calculate the primary clampingforce that corresponds to the steady state operation of the CVT.Expressed in this way, steady state operation of the CVT is athree-degree of freedom problem as three independent variables can bespecified. The steady state of the CVT can also be expressed as atwo-degree of freedom problem in which one of the following parameterscan be specified once the other two are constrained:

1. F₁/F₂: ratio of primary and secondary clamping forces;

2. T_(in)/T_(max): torque ratio; torque input divided by the maximumtransmissible torque for the given transmission ratio and secondaryclamping pressure; and

3. r: the geometric ratio of the transmission.

A 3-D map can be generated to illustrate the relation between thesethree parameters. FIG. 20 is an example of an equilibrium map for theCVT.

A₁/A₂ Ratio

As noted previously, the ratio of the two pulley piston areas isconstrained by the thrust ratio needed to attain all possible ratios andeven more, all possible shift speeds. In a conventional CVT, the ratioA₁/A₂ has to be about 2:1, because of the use of only one source of highpressure. As an example, in a Jatco 2L CVT used for tests, A₁/A₂ wasmeasured and found to be equal to 2.14. The equilibrium map (FIG. 20)demonstrates this statement. In order to obtain a thrust ratio(Fax1/Fax2) of 2, with the primary pressure constrained to be no greaterthan the secondary pressure, the primary pulley piston area has to begreater than that of the secondary pulley by a factor of 2. On the otherhand, when introducing the servo hydraulic control system, two sourcesof high pressure are available, and the piston areas do not have to bedifferent for the CVT to attain all ratios. Furthermore, since the ratioservo pump creates differential pressures between the secondary and theprimary, the pressure difference should be minimized in order tooptimize its work. Also, when A₁/A₂ is different than 1:1, volumes ofboth pistons are different. This means that when the ratio servo pumpmoves fluid from one pulley to the other, in order to shift thetransmission, fluid has to be pumped from or to the sump by the pressureservo pump. Thus a complex relationship between the ratio pump and thepressure pump has to be introduced in the control. On the other hand ifA₁/A₂ is equal to 1, the pressure pump works against the leakage of thesystem in order to hold clamping pressure independently from the actionof the ratio servo pump, whose role is to shift the transmission. Thesephenomena are illustrated in FIG. 21.

Leakage Flow Tests

Leakages are the primary source of control power draw when operating aCVT with a servo controlled hydraulic system. Leakage is defined as thehydraulic fluid flow to be supplied to a pulley cylinder in order tohold a constant pressure in the piston. Leakage flow is proportional topressure and is inherent to the mechanical design of the transmissioncontrol.

Test Conditions:

Both pressures were commanded to 200 PSI. The electric motor throttlewas set to 14.6% and the output speed kept at 800 RPM. During this timethe geometric ratio, the input and output speeds of the CVT and thethrottle command are kept constant: Note that for both motors, positivespeed represents counter clockwise rotation. FIG. 22 illustrates thefluid flow direction that corresponds to a positive P speed and negativeR speed. This happens when both pumps are supplying fluid to theirrespective cylinder, which is the case during this leak test.

By averaging the servo pumps speeds over time, the leak flow of bothsecondary and primary hydraulic circuits can be determined. Theassumption is made that the pumps experience no internal leakage, andthat for every revolution they displace 1.07 cc.

We found that leakages were on the order of 8 times higher in aconventional CVT than in a servo controlled CVT (equivalent to a 5 L)according to the invention. This significant difference results from thedesign of each of these CVTs. A conventional CVT with a stock controlsystem requires leaks for system response. On the other hand, the CVT ofthe present invention was designed for the servo hydraulic control,where leaks are not required and can be minimized in the design. Thecontrol power required for the servo hydraulic system is proportional toleakage flow, and in the ideal case of a zero-leak CVT, it would bereduced to the power required to move fluid from one piston to the otherin order to shift the transmission. The leakage flows observed in theSC-CVT tests indicate a very low control power draw.

Power Draw Measurement Tests

In order to evaluate the power draw of the servo hydraulic controlsystem, two series of tests were performed:

1. Steady state tests in which CVT ratio and secondary pressure are heldconstant.

2. Shifting tests, where Secondary pressure is held constant while theratio is commanded with a step input.

These two series of tests illustrate the different operations of a CVTand provide significant data to understand the energy required by thecontrol system in a CVT equipped with the servo hydraulic systemaccording to the present invention.

Steady State Tests

Steady state tests are used to determine the power required by the CVTto hold secondary pressure and ratio constant at different operatingpoints.

Test Conditions:

The CVT ratio is held at 2.2, 1.0 and 0.7.

The secondary pressure is commanded to 10, 15, 20, 25, 30, 35 and 40bars.

During these tests the measurements of current to the servomotorsamplifiers are used with the voltage of the high voltage bus data tocalculate the electrical power drawn by both servo pumps. The pump speedand pressure are used to compute the hydraulic power for each pump.

In the calculation of the hydraulic power, the assumption is made thatleakage flow exits in the system at 0 psig and that the internal leakageof the pumps is null.

It was found that the electrical current used by the pressure servo pumpamplifier grows with time because the pressure command increases whereasthe current to the ratio amplifier is almost null. As predictedpreviously by the leakage results, the servo controlled CVT usedsignificantly less power than a conventional controlled CVT, eventhought the servo controlled CVT was designed for more than twice thepower/torque capacity.

The reason for this energy usage improvement comes from the mechanicaldesign and components used in the two CVTs. Leak passages were part ofthe design of the conventional CVT cylinders, whereas the servocontrolled CVT cylinders were designed with tight adjustments and noleakage holes.

Shifting Tests

Test Conditions:

For the shifting tests, the electric motor throttle was commanded toregulate the input speed to 800 RPM.

CVT shifting is directly dependent upon the fluid volume displaced fromone piston to the other. The time to shift from overdrive to low gear isequal to the time it takes to shift the other way; and also the ratioresponse to a step input is not linear but slightly curved. This secondpoint is due to the nonlinear, relationship between ratio and runningradii illustrated by equations (16) and (17). The ratio is constrainedby the position of the pulleys which depends on the fluid displaced,dictated by the maximum flow of the servo pump (maximum speed of theratio motor multiplied by pump displacement).

In the servo controlled CVT test configuration, the pulleys movablesheaves could translate 24.81 mm and the effective pressure area was 175cm², so the volume of fluid to be moved to fully shift the CVT was equalto 434 cc. As the pump has a displacement of 1.07 cc/rev and the maximumspeed of the servomotor is about 6000 RPM depending on the voltage ofthe high voltage bus, the servo controlled should execute a full shiftin 4 seconds. A close examination of a full shift indicated that themaximum speed reached by the ratio motor is about 6200 RPM, resulting ina CVT full shift in 3.8 seconds. Integrating the ratio motor speed dataover the time of the full shift, the volume displaced was equal to 422cc. The 8 cc difference between this measurement and the theoreticalnumber can certainly be explained by the leakages in the pump and of thepistons as well as by the experimental error in the data.

Regarding the power necessary to shift the transmission, we observed thecurrent used by the ratio amplifier. By averaging current to theamplifier and voltage of the high voltage bus during the execution ofthe full shift to low gear, the power used by the ratio servo pumpamplifier was found to be 372 watts (for less than 4 seconds). Theshifting speed of the CVT equipped with the servo hydraulic controlsystem was found to be too slow for operating in a conventionalpowertrain using only an internal combustion engine. But it issufficient for use in a parallel hybrid powertrain because instantaneouspower can be supplied by the electric motor while the CVT is commandedto shift. Note that to improve the shifting performance of the servocontrolled CVT, the maximum flow of the ratio servo pump has to beincreased. This can be easily done, if needed, by using a higherdisplacement pump or a faster motor.

Observing the pistons pressures while the servo controlled CVT isshifting, we noted a drop of the primary pressure when the CVT reacheslow gear. The primary movable sheave reached its low gear mechanicallimit but the inertia of the servo pump kept driving fluid out of theprimary piston. We also observed that the ratio pump speed changesdirection to build the primary pressure back. This behavior is specificto shifts toward the lowest possible gear. In order to shift tooverdrive, fluid has to be moved from the secondary piston to theprimary. So when the primary movable sheave reaches the overdrivemechanical stop, the primary pressure observes a pressure peak. In thisgeneration of control algorithm, the torque transmissible through theCVT is regulated using the pressure or clamping servo pump and the ratioclose loop regulation outputs a command for the ratio servo pump.Therefore, the primary pressure is not taken into consideration byeither regulator, which could be dangerous if the axial force on theprimary pulley was getting lower than the minimum presented on FIG. 19.This is difficult to evaluate even though the piston pressure is knownbecause of the dynamic effect and the friction introduced by shiftingthe movable sheaves.

One solution to this problem is to operate the CVT by controlling bothpressures with the two servo pumps and using the equilibrium map toregulate ratio. This will allow for keeping both pressures above theirminimums and using their difference to shift the transmission. The firststep in implementing such a control algorithm is to determineexperimentally the equilibrium map previously discussed.

Experimental Equilibrium Map Determination

In order to experimentally verify the theoretical equilibrium mappreviously described, the SC-CVT was run for various combination ofpressures, ratio and torque. Each steady state or equilibrium point wasthen averaged over its period of steady-state operation and analyzed.FIG. 23 presents some of the data obtained.

The torque input (or torque applied by the electric motor) is evaluatedfrom the maximum torque map provided by the motor manufacturer and thethrottle command. This method is not accurate enough. Ideally, a torquesensor should be positioned between the motor and the CVT input shaft.Due to this inaccurate evaluation of the torque input, the torque ratioterm should be considered with some uncertainty. Nevertheless, theseresults still show the general shape of the equilibrium map. Moreover,by observing FIG. 20, the thrust ratio appears to be more sensitive tothe transmission ratio than it is to torque ratio. Variations of thrustratio are more important when varying the transmission ratio than it iswhen changing the torque ratio.

FIG. 24 shows the experimental data points and the theoreticalequilibrium map. Note that the data points do not appear to, match thecalculated map. The data follow the same trend as the theoretical mapalong the CVT ratio axis, but the slope appears to be more constant.Along the torque ratio axis, the experimental data do not experience amaximum as predicted by the theory. FIG. 25 shows the experimentalresults on the torque ratio-thrust ratio plane for differenttransmission ratio, along with the results of the theory for the sametransmission ratio.

There are several ways to explain the significant difference observedbetween theoretical predictions and experimental results. As notedpreviously, the electric motor torque is not measured, but evaluated.This results in uncertainty in the torque ratio term. The thrust ratiois calculated using the fluid pressure measurements from both cylinders;this considers the effect of static pressure in each cylinder butneglects the effect of dynamic pressure (centrifugal pressure) and theaction of other forces such as friction. Also, the theoreticalpredictions are based on the assumptions that the Eytelwein formuladictates exactly the force distribution in a pulley system and that inthe case of conical pulley, no other phenomenon is taking place. Thecompressive forces in a v-belt are measured along the travel of the beltand the experimental results show a force distribution significantlydifferent from the one predicted by Eytelwein. The coefficient offriction p is also of great importance; small variations in p result insignificant changes in the shape of the theoretical equilibrium map. Forthe previous calculations, μ has been considered constant and equal to0.09 but other researchers have suggested that the coefficient offriction varies with the speed ratio of the transmission.

The experimental data show linear growths in both dimensions(transmission ratio, torque ratio). Therefore the equilibrium map couldbe approximated to a plane.

A best-fit plane was computed from the experimental data. FIG. 26 showsthe different phases of the computation from the data points to thefinal best-fit plane.

Pressure-Based Control Algorithm

The pressure-based control approach is based on the measurement of thecylinders pressure when the CVT is commanded to shift. With the previouscontrol algorithm, shifting command is translated into a required torqueto be applied by the ratio servomotor by moving fluid between the pulleycylinders and creating a pressure differential. This algorithm regulatesthe torque transmissible through the CVT by modulating the secondarypressure, but neglects the primary pressure for this purpose. To shifttoward overdrive, the primary pressure must be raised by pumping fluidto the primary pulley; and to shift toward low gear, the primarypressure is lowered by pumping fluid out of the primary pulley. Thepoint of the pressure-based control algorithm is to use the pressures tocontrol the two states of the CVT (transmission ratio and torquetransmissible). This translates into two requirements. First, thetransmissible torque is evaluated separately for each pulley using thepulley's pressure, and the smaller of the two results is conserved.Second, to shift toward overdrive, the primary pressure is raised; butto shift toward low gear, the secondary pressure is raised instead oflowering the primary pressure. The pressure-based control is a moreconservative algorithm that considers the axial force in each pulleyequal to the static pressure in that pulley cylinder times the activearea of the cylinder. As noted previously, other forces such ascentrifugal pressure, friction or even the dynamic effect of shiftingspeed must be evaluated to determine the actual axial thrust of eachpulley. To operate the CVT by controlling the static pressure of thecylinders, the equilibrium map of the controlled transmission must beknown. The measured equilibrium map will be used to determine the rationeeded between the primary and secondary pressures in order to hold thetransmission ratio constant.

The main steps of the pressure-based control algorithm are illustratedin FIG. 27.

From the experimentally determined equilibrium map, a feed forward valuefor the pressure ratio is determined. In parallel, the controllercomputes a closed loop regulation on the transmission ratio error. Thefeed forward pressure ratio is then multiplied with the output of thetransmission ratio regulator yielding the pressure ratio to becommanded. Using the minimum pressure calculation presented on FIG. 19,the controller derives the minimum pressure to command on each pistonconsidering the operating conditions. Finally, the pistons' pressuresare commanded in accordance with the pressure ratio computed, as well asto ensure that both pressures are greater than or equal to their minima.

This pressure-based control algorithm was programmed into the CVTC andtested on the dynamometer setup. FIG. 28 presents some of the results ofthis testing.

The first thing to observe is that, instead of only using the primarypressure to regulate transmission ratio, either pressure can be raisedabove its minimum in order to shift.

Note that both pressures are kept above a minimum of 200 PSI, even whenshifting the transmission toward low gear. By looking closely at thepressure plot in FIG. 28, one can notice perturbations on the secondarypressure when the primary pressure is raised in order to shift towardlow gear. Similar perturbing phenomena are observed on the primarypressure when the secondary pressure is raised in order to shift towardoverdrive. This problem is inherent to the servo hydraulic controlsystem scheme; the ratio servo pump is dependant upon the operation ofthe pressure servo pump. Therefore, an arrangement such as the one shownin FIG. 29 would be better suited to the pressure based controlalgorithm, as it avoids fluid dependency and perturbation phenomenonbetween the primary and secondary cylinders. The testing performedindicates that the pressure-based control algorithm can be usedsuccessfully to control a CVT, but also shows that the approximation ofthe equilibrium map by a plane is not sufficiently precise. The accuracyof the control of the transmission ratio depends on the precision of themap used for the feed forward pressure ratio. A good solution to thisproblem would be to use a learning controller that would build theequilibrium map while operating the CVT. This seems to be a goodapplication for neural networks.

Macro Slip Experience

During normal operation of the CVT, the commanded torque is kept lowerthan the maximum torque transmissible through the transmission by atorque-clipping algorithm. The role of the torque-clipping algorithm isto throttle back the powertrain if the clamping pressure becomesinsufficient to transmit the torque requested by the driver. Even withthis algorithm working properly, macro slip of the chain was observedwhile testing the transmission on the dynamometer. FIG. 30 illustratesan occurrence of macro slip, the bottom plot shows the transmissionratio (lower solid line) read from the sheave position measurement(geometric ratio) and the calculated ratio (upper dashed line) usinginput and output speed signals (speed ratio). At time 83 seconds, theinput speed increases whereas the output speed decreases; this istypical of a slip under positive torque. The input and output aredecoupled for an instant. This allows the motor to accelerate the inputwhile the load decelerates the output.

This unexpected slip of the chain raised questions about the reliabilityof the torque command estimation. As discussed previously, the electricmotor torque is considered equal to the throttle commanded (in %) timesthe maximum torque for the given rotational speed. Looking at the testdata at the time of the slip, the electric motor torque commanded was140 Nm, but the dynamometer measured 180 Nm. The transmission ratio was1:1; therefore the output torque cannot be greater than the torqueinput. In fact the torque output should be in the order of 3 to 5% lessthan the input torque due to the SC-CVT transmission efficiency. Itappears here that the electric motor was producing almost 30% moretorque than expected. There are several possible explanations for thistorque difference:

1. A linear relationship between the throttle and the torque wasassumed;

2. The communication of the throttle from the CVT Controller to themotor inverter is made through analog channels; electro-magnetic noiseand ground reference offset could cause problems;

3. The maximum torque line of the electric motor provided by the motormanufacturer is given for a high voltage bus at 336 volts, but thebattery pack voltage used to supply power to the electric motor variesbetween 400 volts and 260 volts depending on the load applied and thebattery state of charge (SOC).

CONCLUSIONS

CVTs have many advantages over discrete geared transmissions, and havealready proven the benefits of their use in conventional automotivepowertrain. Two types of CVTs appear to be suitable for cars and trucks:toroidal traction drive and belt/chain drive. Toroidal CVTs still remainat a development stage, and numerous issues have to be addressed beforethey can be placed on the market. On the other hand, belt CVTs arealready found in many commercial vehicles. The recent introduction ofchains to replace the commonly used VDT metal push belt can extend theuse of belt type CVTs to full size sedans and sport utility vehicles(SUV).

The SC-CVT is a good illustration of belt type CVT development; thistransmission using a chain has been designed for a full size SUV. TheSC-CVT has met its design criteria for high power and torque capacitiesand has shown great potential. Testing performed in the truckdemonstrated the success of this project. The servo hydraulic systemimplemented to control the SC-CVT has been functioning to expectations,and the test vehicle exhibited good drivability throughout the testing.A theoretical study of CVT behavior was conducted in order to betterunderstand the control requirements of the SC-CVT. Based on the theoryof Eytelwein, a series of calculations were presented to characterizethe relationship between torque input, clamping forces and transmissionratio. It should be appreciated that inertia is an importantconsideration in that the ratio rate can set the torque, but the torquethat the ratio rate sets is dependent on the inertia of the engine andthe inertia of the output or the inertia of the car. In other words, fora given ratio rate the torque that the CVT transmits is a function ofthe inertias on the input and output.

The servo hydraulic control scheme used for the SC-CVT has been shown towork very well. This scheme uses a control algorithm that regulatesclamping pressure using the pressure servo pump, and closes the loop onratio by commanding the ratio servo pump. This version of controlalgorithm resulted in safe operation of the CVT, though the primarypressure can become lower than the static theoretical minimum pressure.

The SC-CVT, due to low internal leakage, has been shown to require verylow control power using servo hydraulic control. The power consumed bythe two servomotors is below 100 watts for most of the steady stateoperating conditions. Even when compared, for various steady states ofpressure and ratio, with a production CVT modified to use the same servohydraulic control system, the servomotors of the SC-CVT used 5 timesless electrical power than the one installed on the conventional CVT.This demonstrates the benefits of designing a transmission specificallyfor the servo hydraulic control system. One of the main differencesbetween the SC-CVT and regular production CVTs is the use of equal areapistons for the primary and secondary pulleys. This design modificationbrings many advantages: it reduces control complexity by avoidingclamping pressure perturbation when shifting; it lowers the averageratio servo pump energy usage by operating naturally closer to theequilibrium map; and because parts are identical for both pulleys, itdecreases manufacturing cost.

A control algorithm based on regulating pressures was developed usingexperimental equilibrium map data and tested to control the SC-CVT.Pressure-based control has shown promising results in terms offeasibility, but could benefit from a more adapted hydraulic controlscheme where each servo pump supplies a pulley piston independently fromthe other one. It was also found that a learning controller could beimplemented to establish the precise equilibrium map of the controlledCVT.

The test results presented above lead to the following observations forimprovements that can be pursued:

1. In order to control clamping pressure more closely, the input torqueto the CVT should be accurately known. This requires either ameasurement of motor output torque or a reliable map of the maximum EMtorque envelop as a function of bus voltage.

2. Components used for the servo hydraulic control system should besized in accordance to their actual operation requirements. Using theresults of the power draw testing, amplifiers could be significantlydownsized, the pressure servo pump could use a slower motor or lowerdisplacement pump, whereas the ratio servo pump, depending on thedesired shift speed, could use a higher displacement pump.

3. Further study of the possible occurrence of macro-slip should beperformed when better knowledge of the EM torque is available to thecontrol algorithm. Changes in the algorithm should then be considered ifmacro-slip occurs. Additionally, slowing down the ratio motor whenapproaching mechanical limits or increasing the secondary pressurecommand while shifting towards low gear should be considered.

4. The mechanical efficiency of the SC-CVT should be measured. Thiswould require accurate torque and speed measurements on both input andoutput of the transmission or the construction of a specialfour-quadrant dynamometer.

5. Finally, measurement of chain speed in addition to pulleys speedscould lead to research on micro slip of the chain and on clampingpressure scheduling.

Although the description above contains many details, these should notbe construed as limiting the scope of the invention but as merelyproviding illustrations of some of the presently preferred embodimentsof this invention. Therefore, it will be appreciated that the scope ofthe present invention fully encompasses other embodiments which maybecome obvious to those skilled in the art, and that the scope of thepresent invention is accordingly to be limited by nothing other than theappended claims, in which reference to an element in the singular is notintended to mean “one and only one ” unless explicitly so stated, butrather “one or more.” All structural, chemical, and functionalequivalents to the elements of the above-described preferred embodimentthat are known to those of ordinary skill in the art are expresslyincorporated herein by reference and are intended to be encompassed bythe present claims. Moreover, it is not necessary for a device or methodto address each and every problem sought to be solved by the presentinvention, for it to be encompassed by the present claims. Furthermore,no element, component, or method step in the present disclosure isintended to be dedicated to the public regardless of whether theelement, component, or method step is explicitly recited in the claims.No claim element herein is to be construed under the provisions of 35U.S.C. 112, sixth paragraph, unless the element is expressly recitedusing the phrase “means for.

TABLE 1 SC-CVT Parameters Parameter Value Unit Description CD 250 mmPulleys' centre to centre distance A1, A2 175 cm² Effective pulleypressure area RedEM 2.4545 Gear ratio between EM and input pulley Rmax2.2556 Maximum transmission ratio (Low Gear) Rmin 0.4433 Minimumtransmission ratio (OD) β 11 ° Sheave angle R1max, R2max 114.7 mmMaximum running radii R1min, R2min 50.85 mm Minimum running radii Lchain1036.5 mm Chain length when wrapped around the pulleys Pitch 13.65 mmChain pitch Npitch 75 Numbers of pitches Wchain 44.4 mm Chain width

1. A method for controlling the operation of a continuously variabletransmission (CVT), comprising: mapping rate of change of ratio toclamping pressure and/or differential pressure between pulleys in a CVT;controlling clamping pressure and/or differential pressure betweenpulleys in said CVT based on said mapping; and controlling torque to beapplied to a primary pulley in the CVT to a level that the clampingpressure is sufficient to avoid slipping with a torque clippingalgorithm; wherein torque applied to the primary pulley will not exceedthe capacity of the CVT pulleys to avoid slipping.
 2. A method foroptimizing the operation of a continuously variable transmission (CVT),comprising: accessing a map of the relationship between pressure of aCVT and rate of change of ratio to transmit a given amount of torque;controlling primary and second pulley pressure of the CVT to achieve acommanded clamping pressure for commanded torque and ratio rate based onsaid map; and controlling torque to be applied to a primary pulley inthe CVT to a level that the clamping pressure is sufficient to avoidslipping with a torque clipping algorithm; wherein torque applied to theprimary pulley will not exceed the capacity of the CVT pulleys to avoidslipping.
 3. A method for optimizing the operation of a continuouslyvariable transmission (CVT), comprising: controlling primary andsecondary pulley pressures of the CVT to control the ratio rate and/orratio and clamping pressure of the CVT based on an equilibrium ratio mapof the CVT specifying the relationship between the ratio of primary andsecondary clamping forces, torque ratio and geometric ratio of thetransmission; and controlling torque to be applied to a primary pulleyin the CVT to a level that the clamping pressure is sufficient to avoidslipping with a torque clipping algorithm; wherein torque applied to theprimary pulley will not exceed the capacity of the CVT pulleys to avoidslipping.
 4. A method for controlling the operating of a continuouslyvariable transmission (CVT) comprising: providing a servo controlsystem; said servo control system configured to control clampingpressure and differential pressure between primary and secondary pulleysin the CVT; controlling said servo control system to achieve commandedclamping pressure and/or differential pressure between the primary andsecondary pulleys based on a mapping of rate of change of ratio of saidCVT to said clamping pressure and/or differential pressure betweenpulleys; and controlling torque to be applied to a primary pulley in theCVT to a level that the clamping pressure is sufficient to avoidslipping with a torque clipping algorithm; wherein torque applied to theprimary pulley will not exceed the capacity of the CVT pulleys to avoidslipping.